Racah matrices and \(6j\) -symbols have quite a long history in science. They first appeared in physics through the studies of angular momenta [1]}, where they describe transformation between different couplings of three particles. Racah matrices appearing in this problem are actually quite simple and well studied. However, in mathematical terms this angular momenta problem actually corresponds to the multiplication of different representations of the \(SU(2)\)  algebra. In this language Racah coefficients appear when one takes a product of three representations and expands it as a sum of irreducible representations:
\(T_1\otimes T_2 \otimes T_3=\sum M_{12}^{1,2} Q_{12} \otimes T_3= \sum N^{12,3}M_{12}^{1,2} Q.\) 
